2028 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 42, NO. 11, NOVEMBER 1995

Band gap (eV) Electron effective mass

Brief

1.4+ 1 . 2 4 ~ (0.067 4- 0 . 0 8 3 ~ h

Early Voltage in Double Heterojunction Bipolar Transistors

Dielectric constant

M. M. Jahan and A. F. M. Anwar

(13.1 - 3 ~ ) ~ o

Abstract-The Early voltage for abrupt double heterojunction bipolar transistors (DHBT's) has been calculated by using an effective junction velocity (S,) at the base-collector heterojunction. S, is obtained by self- consistently partitioning thermionic and quantum mechanical tunneling currents. Unlike single heterojunction bipolar transistors (SHBT's), the Early voltage varies very rapidly at low reverse bias and approaches the SHBT-limit at sufficiently high reverse bias. This is attributed to the presence of energy barrier at the b-c heterojunction.

I. INTRODUCTION Owing to its very high power handling capability and excellent

power added efficiency (PAE), heterojunction bipolar transistors (HBT's) have become the most popular compound semiconductor device for the microwave and millimeter-wave applications in the recent time [ 11. Many of these applications (e.g., mobile telephones, personal communication systems (PCS), etc.) require a high degree of linearity between the input and output within the range of operation [l]. One of the major source of nonlinearity in bipolar transistors is due to the base width modulation [2] (Early effect) as a function of the base-collector (b-c) junction voltage. The Early voltage ( v ~ ) is a measure of the base width modulation and should be as high as possible for linear operation. Grinberg and Luryi [3] have shown that for sufficiently large conduction band discontinuity at the emitter-base (e-b) junction, the Early effect is virtually nonexistent (i.e., I A = cc) in single heterojunction bipolar transistors (SHBT's).

DHBT's have greater base-collector (b-c) junction breakdown voltage, these are well suited for high power application and con- sequently, the study of the Early voltage, which is a measure of the linearity of the device, has become even more important for DHBT's. However, the analysis of the Early voltage in the context of double heterojunction bipolar transistors (DHBT's) has not yet been reported and is the topic of the present paper.

In SHBT's, it is argued that the current transport across the emitter- base (e-b) junction is the bottleneck in determining the total collector current for a sufficiently high band discontinuity at the e-b junction [3]. In abrupt DHBT's, however, the bottleneck may also be the transport across the b-c heterojunction [4]. Under these circumstances, the Early voltage depends not only on the base width modulation but also on the modulation of the b-c junction energy barrier. In the present paper, the Early voltage for DHBT's is studied in terms of the effective b-c junction velocity [5] which carries the signature of the modulation of the energy bamer at the b-c junction. It is shown that for the special case when the effective height of the b-c junction energy barrier is zero, the Early voltage of DHBT's reaches the SHBT-limit.

Manuscript received November 28, 1994. The review of this brief was

The authors are with the Department of Electrical and Systems Engineering,

IEEE Log Number 9414589.

arranged by Associate Editor P. M. Solomon.

The University of Connecticut, Storrs, CT 06269-3157 USA.

TABLE I MATERIAL PARAMETERS USED IN THE SIMULATION

I Parameters I Expression I

"

cn I 8.854 x 10-14F/cm 1 _ _ _ ~ Y

Thermal velocity ( w a ) I 1.5 x 107mp 1 11. THEORY

The collector current for DHBT's is given as [4]

where nO0 is the equilibrium minority carrier concentration at the edge of the e-b junction depletion region on the emitter side, I h is the e-b junction forward bias, Se (S,) is the emitter (collector) junction velocity, W is the quasi neutral base width, D, is the diffusivity of the minority carrier at the base, k is the Boltzmann constant, q is the elementary electronic charge and T is the temperature in OK. In SHBT's and BJT's, SC is assumed to be x [3] or thermal velocity Vth [6]. Roulston [6] has shown that the use of s, = x) rather than Sc = 'Uth may render an underestimation of VA . In DHBT's, S, may vary significantly from Vth due to the coexistence of the thermionic and tunneling currents at the b-c heterojunction and thus the use of an exact S, proves to be even more critical in determining 1.-4. The use of ( I ) together with a physics-based model for S, will allow one to compute I.2 for DHBT. For a given e-b junction forward bias, se is constant and the Early voltage ( - J c / k [6]) becomes

where

(3)

zp being the depletion region width of the b-c junction on the base side

(4)

with -vdO is the collector doping concentration, € I , ( € , ) is the base (collector) dielectric constant, and I the built-in voltage

where n l p ( n r n ) is the intrinsic carrier concentration on the base (collector) side, and AE, is the amount of offset of the intrinsic fermi levels between the narrower bandgap base and the wider bandgap collector sides.

0018-9383/95$04.00 0 1995 IEEE

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 42, NO. 11. NOVEMBER 1995 2029

20000000

n [II \ 6 16000000 0

h 4 4

r( : 12000000 : C 0

d 3 8000000

? c,

4000000

, , I , , , ,

0

0 2 4 6 8 10

Base-collector junction reverse bias (V)

Fig. 1. The pertinent data are described in the text.

The b-c junction velocity as a function of b-c junction reverse bias.

For SHBT’s, the above expression of the Early voltage may be simplified by replacing S, with the thermal velocity and using

s, = x. __- d & ic = 0. The classical BJT-limit [6] can be obtained by putting

111. RESULTS AND DISCUSSIONS The following discussion is based on Al,Gal-,As/GaAs/

Al,Gal-,As DHBT’s. The doping of emitter (-Ve), base ( - V a o ) and collector (-\?do) are 3 x 101‘/cm3. 10i9/cm3 and 5 x 10”/cm3, respectively. The base width is 0.05 ,um and D , = 30 cm2/S. The conduction band discontinuity at the b-c junction is 0.2 eV. The pertinent material parameters are shown in Table 1. The simulation is performed at T = 300°K. The e-b junction bias is assumed to be 1.4 V.

In Fig. 1, the b-c junction velocity S, is plotted as a function of b-c reverse bias for a DHBT with p ( = -Yao/-Vd0) as a parameter. S, is obtained by recognizing the thermionic and tunneling components of the collector current and partitioning it quantum mechanically as is discussed in [5] . In order to estimate the exact quantum mechanical calculation to a first order approximation, S, may also be expressed by the following empirical relationship obtained by fitting the S, - Vbc curve for -’LTa0 = 10i9/cm3 and -Vdo = 5 x 10”/cm3 ( p = 20) as

Fig. 2 shows the calculated 12 by assuming S, = x (classical BJT-limit), S, = I’th (SHBT-limit [3]), and (4) (DHBT-limit). Since the main interest is to investigate the effect of the S, on V4, the e-b junction is considered to be under a constant bias of 1.4 volt corresponding to S, = 10’ cm/S. As observed, there exists a significant deviation of the DHBT-limit of V4 from the other limits especially at low reverse bias. \:4, for DHBT’s, at low reverse bias (across the b-c junction) is very small compared to the other limits of the Early voltage. Also V i in the DHBT-limit shows a sharper

v ,h(o .4(1 - 4.38e-’.’‘bC) + 0.6).

1500

h

v + 1000

: Q) hll m z h Ll a~ 500 w r(

0

0 2 4 6 8 10

Base-collector reverse bias (V)

Fig. 2. For comparison, the SHBT and BJT limits are also shown.

The Early voltage is plotted as function of b-c junction reverse bias.

rise as a function of b-c junction reverse bias as compared to the other limits. These behaviors are solely attributed to the presence of effective energy barrier at the b-c heterojunction. As the bias voltage is increased, the energy barrier gets quenched and the velocity at the b-c junction approaches the thermal velocity. At sufficiently high reverse bias, the effective energy barrier completely disappears and VA at DHBT-limit approaches that at SHBT-limit.

IV. CONCLUSION

The Early voltage in DHBT’s has been studied by using the junction velocity which is obtained by partitioning the total collector current into its constituents, namely thermionic and tunneling com- ponents. Unlike SHBT’s, the Early voltage in DHBT’s is relatively smaller at low reverse bias and increases sharply as the reverse bias is increased. At sufficiently high reverse bias when the energy barrier at the b-c junction completely disappears, the Early voltage of DHBT’s approaches that of SHBT’s.

REFERENCES

[I] K. Fricke, G. Gatti, H. L. Hartnagel, V. Krozer, and J. Wufl, “Per- formance capabilities of HBT devices and circuits for satellite com- munication,” IEEE Trans. Microwave Theon. Tech., vol. 40, p. 1205, 1992.

[2] J. M. Early, “Effects of space-charge layer widening in junction transis- tors,” in Proc. IRE, vol. 42, 1954, p. 1761.

[3] A. A. Grinberg and S. Luryi, “Dynamic Early effect in heterojunction bipolar transistors,” IEEE Elecrron Device Lerr . , vol. 14, p. 292, 1993.

[4] M. S. Lundstrom, “An Ebers-Moll model for the heterostructure bipolar transistor,” Solid-Sfare Electron., vol. 29, p. 1173, 1986.

[5] M. M. Jahan and A. F. M. Anwar, “An exact current partitioning and its effect on base transit time in double heterojunction bipolar transistors,” submitted to Solid-State Electron.

[6] D. J. Roulston, “Early voltage in very-narrow-base bipolar transistor,” IEEE Elecrron Device Lett., vol. 11, p. 88, 1990.